40. والتخطيط ةراإلدا مبادئد.ياملصر محمدكمال 40
A calculator company produces a scientific calculator and a graphingcalculator.
Long-term projections indicate an expected demand of at least 100 scientific and 80
graphingcalculators each day.
Because of limitationson production capacity, nomore than200 scientific and 170
graphing calculators can be made daily.
To satisfy a shipping contract, a total of at least 200 calculators much be shipped
each day.
If eachscientific calculator sold resultsin a $2 loss, but eachgraphing calculator
produces a $5 profit, how manyof each type should be made dailyto maximizenet
profits?
The question asks for the optimalnumber of calculators,so my variableswill stand
for that:
◦ x: numberof scientific calculatorsproduced
y:numberof graphingcalculatorsproduced
41. والتخطيط ةراإلدا مبادئد.ياملصر محمدكمال 41
Since they can't produce negative numbers of calculators, I have
the two constraints, x> 0 and y> 0. Butin this case, I can ignore
these constraints, because I already have thatx> 100 and y> 80.
The exercise also gives maximums: x< 200 and y< 170.
The minimum shipping requirementgivesme x+ y> 200; in other
words,y> –x+ 200.
The profit relation will be my optimization equation: P= –2x+ 5y.
So the entire system is:
P= –2x + 5y(Maxprofit), subject to:
100 < x< 200 (expected demand)
80 < y< 170 (expected demand)
y> –x+ 200 (minimum shipment)
ملاحظة : النظام يتكون من عدة أجزاء منفصلة تتعاون فيما بينها لإنتاج شيء معين. ويمكن تقسيم الأنظمة إلى عدة أنواع حسب معايير مختلفة. وبحسب درجة الانفتاح، هناك نوعان من الأنظمة، فقد يكون النظام مفتوحًا يتفاعل مع البيئة الخارجية، وقد يكون مغلقا.